Chapter 1: Q63. (page 46)

set on a number line.Solve each inequality. Describe the solution set using set builder or interval notation. Then graph the solution
63. $3 n + 4 (n + 3) < 5 (n + 2)$

Short Answer

Expert verified

Solution set of inequality is $(- \infty, - 1)$ .

Solution set on number line is

Step by step solution

- Write properties of inequality.

Properties of inequalities are written in following table:

- Solve 3n+4n+3<5n+2.

To solve given inequality, use subtraction and division properties of inequality. To solve given inequality, expand the parentheses on each side. Subtract 12 from each side then subtract $5 n$ from each side and then divide each side of the inequality by 2

$\begin{array}{l} 3 n + 4 n + 12 < 5 n + 10 \\ 7 n + 12 - 12 < 5 n + 10 - 12 \\ 7 n - 5 n < 5 n - 2 - 5 n \\ \frac{2 n}{2} < \frac{- 2}{2} \\ n < - 1 \end{array}$

Thus, solution is $n < - 1$ .

– Describe solution set in interval notation.

Assolution set of the inequality is all real numbers less than $- 1$ .

Write the solution set in interval notation.

$(- \infty, - 1)$

– Graph the solution set

Open circle on $- 1$ shows this point is excluded in the solution set

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set on a number line.Solve each inequality. Describe the solution set using set builder or interval notation. Then graph the solution
63. $3 n + 4 (n + 3) < 5 (n + 2)$

Short Answer

Step by step solution

- Write properties of inequality.

- Solve 3n+4n+3<5n+2.

– Describe solution set in interval notation.

– Graph the solution set

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set on a number line.Solve each inequality. Describe the solution set using set builder or interval notation. Then graph the solution63. 3n+4n+3<5n+2

Short Answer

Step by step solution

- Write properties of inequality.

- Solve 3n+4n+3<5n+2.

– Describe solution set in interval notation.

– Graph the solution set

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Probability and Statistics

Logic and Functions

Geometry

Applied Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

set on a number line.Solve each inequality. Describe the solution set using set builder or interval notation. Then graph the solution
63. $3 n + 4 (n + 3) < 5 (n + 2)$